Multimode resonances, intermode bound states, and bound states in the continuum in waveguides

Abstract

We study analytically and numerically the formation of bound states in the continuum (BICs) in quantum-mechanical and optical spatially symmetric multimode waveguide systems. The widely used Friedrich-Wintgen model predicts a BIC for two (nearly) degenerate eigenstates of the resonator. However, numerical calculations typically show that BICs may appear away from the degeneracy point (or avoided crossing region) in the energy-parameter space. From the two-mode point of view based on the Friedrich-Wintgen model, such BICs can be considered as accidental. In this paper, we go beyond the two-mode approximation and, appealing to the notion of intermode bound states, provide an illustrative procedure for deriving conditions for BIC formation within an arbitrary finite-mode approximation. In particular, we show that a three-mode approximation allows the description of a continuous transition of a BIC between different pairs of modes, which can be associated with it within the two-mode model. Also, a manifestation of exceptional points as (anti)resonance coalescence is discussed. Analytical conclusions are verified by the results of numerical simulations of two-dimensional quantum-mechanical and optical stubbed waveguides with confining impurities in the stub. Moreover, numerical simulations confirm the existence of BICs in optical subwavelength resonators, which were earlier predicted in quantum-mechanical waveguides.